Abstract

We study unit circles of polygonal Radon planes from a geometric point of view. In particular, we prove that a two-dimensional real polygonal Banach space X\mathbb{X} cannot be a Radon plane if the number of vertices of its unit circle is 4n, for some natural number n. Also we obtain a complete characterization of polygonal Radon planes in terms of a tractable geometric concept introduced in this article. It follows from our characterization that every regular polygon with 4n+2 vertices, where n is a natural number, is the unit circle of a Radon plane. Furthermore, we describe types of Radon planes for which the unit circles are hexagons, but not regular ones.

Author information

Contact details are reproduced from the original publication and may be historical.

Kallol Paul

Department of Mathematics, Jadavpur University, Kolkata 700032, India

kalloldada@gmail.com

Keywords

  • Radon plane
  • Birkhoff-James orthogonality
  • polygonal Banach space

Mathematics Subject Classification

46B20; 52A21

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Suggested citation

K. Mandal, D. Sain, K. Paul. “A Geometric Characterization of Polygonal Radon Planes.” Journal of Convex Analysis 26 (2019), No. 4, 1113–1123. https://doi.org/10.68381/jca26061

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.